Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,68,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 68, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 68);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 68 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(255.861316737\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 3 x^{5} + \cdots - 80\!\cdots\!00 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{46}\cdot 3^{29}\cdot 5^{6}\cdot 7^{2}\cdot 11^{2}\cdot 13\cdot 17 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.58092e9\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17747e10 | −0.969272 | −0.484636 | − | 0.874716i | \(-0.661048\pi\) | ||||
−0.484636 | + | 0.874716i | \(0.661048\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.92992e18 | −0.0605115 | ||||||||
\(5\) | −8.66624e22 | −0.332917 | −0.166458 | − | 0.986048i | \(-0.553233\pi\) | ||||
−0.166458 | + | 0.986048i | \(0.553233\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.38994e28 | 1.65732 | 0.828662 | − | 0.559749i | \(-0.189102\pi\) | ||||
0.828662 | + | 0.559749i | \(0.189102\pi\) | |||||||
\(8\) | 1.84279e30 | 1.02792 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.02043e33 | 0.322687 | ||||||||
\(11\) | 2.84875e34 | 0.369827 | 0.184914 | − | 0.982755i | \(-0.440799\pi\) | ||||
0.184914 | + | 0.982755i | \(0.440799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.77669e36 | 0.278341 | 0.139170 | − | 0.990268i | \(-0.455556\pi\) | ||||
0.139170 | + | 0.990268i | \(0.455556\pi\) | |||||||
\(14\) | −3.99156e38 | −1.60640 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.03805e40 | −0.935827 | ||||||||
\(17\) | 1.58934e41 | 0.957587 | 0.478793 | − | 0.877928i | \(-0.341074\pi\) | ||||
0.478793 | + | 0.877928i | \(0.341074\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.30638e43 | 1.89594 | 0.947972 | − | 0.318354i | \(-0.103130\pi\) | ||||
0.947972 | + | 0.318354i | \(0.103130\pi\) | |||||||
\(20\) | 7.73889e41 | 0.0201453 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.35432e44 | −0.358463 | ||||||||
\(23\) | −5.95710e44 | −0.143599 | −0.0717997 | − | 0.997419i | \(-0.522874\pi\) | ||||
−0.0717997 | + | 0.997419i | \(0.522874\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.02523e46 | −0.889166 | ||||||||
\(26\) | −6.80189e46 | −0.269788 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.02719e47 | −0.100287 | ||||||||
\(29\) | 1.88314e48 | 0.192553 | 0.0962763 | − | 0.995355i | \(-0.469307\pi\) | ||||
0.0962763 | + | 0.995355i | \(0.469307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.76621e49 | −1.06932 | −0.534662 | − | 0.845066i | \(-0.679561\pi\) | ||||
−0.534662 | + | 0.845066i | \(0.679561\pi\) | |||||||
\(32\) | −3.19730e49 | −0.120853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.87140e51 | −0.928162 | ||||||||
\(35\) | −2.93780e51 | −0.551751 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00773e52 | −0.586067 | −0.293034 | − | 0.956102i | \(-0.594665\pi\) | ||||
−0.293034 | + | 0.956102i | \(0.594665\pi\) | |||||||
\(38\) | −1.53823e53 | −1.83769 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.59701e53 | −0.342213 | ||||||||
\(41\) | −1.76167e54 | −1.65069 | −0.825344 | − | 0.564631i | \(-0.809019\pi\) | ||||
−0.825344 | + | 0.564631i | \(0.809019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65878e54 | 1.07530 | 0.537650 | − | 0.843168i | \(-0.319312\pi\) | ||||
0.537650 | + | 0.843168i | \(0.319312\pi\) | |||||||
\(44\) | −2.54391e53 | −0.0223788 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.01432e54 | 0.139187 | ||||||||
\(47\) | −1.13424e56 | −1.09503 | −0.547515 | − | 0.836796i | \(-0.684426\pi\) | ||||
−0.547515 | + | 0.836796i | \(0.684426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.30791e56 | 1.74672 | ||||||||
\(50\) | 7.09453e56 | 0.861844 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.15854e55 | −0.0168428 | ||||||||
\(53\) | −5.57999e57 | −0.962481 | −0.481240 | − | 0.876589i | \(-0.659814\pi\) | ||||
−0.481240 | + | 0.876589i | \(0.659814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.46879e57 | −0.123122 | ||||||||
\(56\) | 6.24694e58 | 1.70360 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.21734e58 | −0.186636 | ||||||||
\(59\) | −2.54355e59 | −1.20753 | −0.603764 | − | 0.797163i | \(-0.706333\pi\) | ||||
−0.603764 | + | 0.797163i | \(0.706333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.65006e59 | −0.722619 | −0.361309 | − | 0.932446i | \(-0.617670\pi\) | ||||
−0.361309 | + | 0.932446i | \(0.617670\pi\) | |||||||
\(62\) | 1.14994e60 | 1.03647 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.38410e60 | 1.05297 | ||||||||
\(65\) | −5.00622e59 | −0.0926643 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.13257e59 | 0.0478344 | 0.0239172 | − | 0.999714i | \(-0.492386\pi\) | ||||
0.0239172 | + | 0.999714i | \(0.492386\pi\) | |||||||
\(68\) | −1.41927e60 | −0.0579450 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.45918e61 | 0.534797 | ||||||||
\(71\) | −1.41637e62 | −1.36152 | −0.680759 | − | 0.732507i | \(-0.738350\pi\) | ||||
−0.680759 | + | 0.732507i | \(0.738350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.86823e62 | −1.08717 | −0.543587 | − | 0.839353i | \(-0.682934\pi\) | ||||
−0.543587 | + | 0.839353i | \(0.682934\pi\) | |||||||
\(74\) | 2.36405e62 | 0.568059 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.16659e62 | −0.114726 | ||||||||
\(77\) | 9.65708e62 | 0.612924 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.81077e63 | 0.755646 | 0.377823 | − | 0.925878i | \(-0.376673\pi\) | ||||
0.377823 | + | 0.925878i | \(0.376673\pi\) | |||||||
\(80\) | 1.76622e63 | 0.311553 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.07431e64 | 1.59997 | ||||||||
\(83\) | −3.57371e64 | −1.83655 | −0.918275 | − | 0.395942i | \(-0.870418\pi\) | ||||
−0.918275 | + | 0.395942i | \(0.870418\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.37736e64 | −0.318797 | ||||||||
\(86\) | −6.66306e64 | −1.04226 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.24964e64 | 0.380154 | ||||||||
\(89\) | −2.86517e64 | −0.142097 | −0.0710486 | − | 0.997473i | \(-0.522635\pi\) | ||||
−0.0710486 | + | 0.997473i | \(0.522635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.95826e65 | 0.461301 | ||||||||
\(92\) | 5.31964e63 | 0.00868941 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.33553e66 | 1.06138 | ||||||||
\(95\) | −1.13215e66 | −0.631192 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.69701e66 | 1.30307 | 0.651536 | − | 0.758618i | \(-0.274125\pi\) | ||||
0.651536 | + | 0.758618i | \(0.274125\pi\) | |||||||
\(98\) | −8.60485e66 | −1.69305 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.38048e65 | 0.0538048 | ||||||||
\(101\) | −1.32619e67 | −0.950253 | −0.475127 | − | 0.879917i | \(-0.657598\pi\) | ||||
−0.475127 | + | 0.879917i | \(0.657598\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.08115e67 | 0.401643 | 0.200821 | − | 0.979628i | \(-0.435639\pi\) | ||||
0.200821 | + | 0.979628i | \(0.435639\pi\) | |||||||
\(104\) | 1.06452e67 | 0.286113 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.57029e67 | 0.932906 | ||||||||
\(107\) | 1.18331e68 | 1.22671 | 0.613356 | − | 0.789806i | \(-0.289819\pi\) | ||||
0.613356 | + | 0.789806i | \(0.289819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.33578e68 | −0.744643 | −0.372321 | − | 0.928104i | \(-0.621438\pi\) | ||||
−0.372321 | + | 0.928104i | \(0.621438\pi\) | |||||||
\(110\) | 2.90694e67 | 0.119338 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.90887e68 | −1.55097 | ||||||||
\(113\) | −1.37803e68 | −0.229683 | −0.114842 | − | 0.993384i | \(-0.536636\pi\) | ||||
−0.114842 | + | 0.993384i | \(0.536636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.16257e67 | 0.0478066 | ||||||||
\(116\) | −1.68163e67 | −0.0116516 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.99496e69 | 1.17042 | ||||||||
\(119\) | 5.38777e69 | 1.58703 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.12195e69 | −0.863228 | ||||||||
\(122\) | 5.47532e69 | 0.700414 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.72115e68 | 0.0647064 | ||||||||
\(125\) | 1.10941e70 | 0.628935 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.20969e70 | 0.402949 | 0.201475 | − | 0.979494i | \(-0.435427\pi\) | ||||
0.201475 | + | 0.979494i | \(0.435427\pi\) | |||||||
\(128\) | −3.51285e70 | −0.899758 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.89468e69 | 0.0898169 | ||||||||
\(131\) | −7.83782e70 | −0.923862 | −0.461931 | − | 0.886916i | \(-0.652843\pi\) | ||||
−0.461931 | + | 0.886916i | \(0.652843\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.42856e71 | 3.14219 | ||||||||
\(134\) | −8.39840e69 | −0.0463645 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.92882e71 | 0.984326 | ||||||||
\(137\) | 3.50919e71 | 0.922716 | 0.461358 | − | 0.887214i | \(-0.347362\pi\) | ||||
0.461358 | + | 0.887214i | \(0.347362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.51334e71 | −0.568492 | −0.284246 | − | 0.958751i | \(-0.591743\pi\) | ||||
−0.284246 | + | 0.958751i | \(0.591743\pi\) | |||||||
\(140\) | 2.62344e70 | 0.0333873 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.66774e72 | 1.31968 | ||||||||
\(143\) | 1.64563e71 | 0.102938 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.63197e71 | −0.0641040 | ||||||||
\(146\) | 3.37727e72 | 1.05377 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.79289e71 | 0.0354638 | ||||||||
\(149\) | −2.55470e72 | −0.403273 | −0.201636 | − | 0.979460i | \(-0.564626\pi\) | ||||
−0.201636 | + | 0.979460i | \(0.564626\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.10289e72 | 0.919288 | 0.459644 | − | 0.888103i | \(-0.347977\pi\) | ||||
0.459644 | + | 0.888103i | \(0.347977\pi\) | |||||||
\(152\) | 2.40739e73 | 1.94889 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.13709e73 | −0.594090 | ||||||||
\(155\) | 8.46364e72 | 0.355996 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.13316e72 | 0.113147 | 0.0565736 | − | 0.998398i | \(-0.481982\pi\) | ||||
0.0565736 | + | 0.998398i | \(0.481982\pi\) | |||||||
\(158\) | −3.30961e73 | −0.732426 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.77086e72 | 0.0402341 | ||||||||
\(161\) | −2.01942e73 | −0.237991 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.44265e73 | −0.502088 | −0.251044 | − | 0.967976i | \(-0.580774\pi\) | ||||
−0.251044 | + | 0.967976i | \(0.580774\pi\) | |||||||
\(164\) | 1.57316e73 | 0.0998856 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.20794e74 | 1.78012 | ||||||||
\(167\) | −4.51496e74 | −1.56190 | −0.780949 | − | 0.624595i | \(-0.785264\pi\) | ||||
−0.780949 | + | 0.624595i | \(0.785264\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.97359e74 | −0.922526 | ||||||||
\(170\) | 1.62180e74 | 0.309001 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.05325e73 | −0.0650680 | ||||||||
\(173\) | −1.01593e75 | −1.07726 | −0.538629 | − | 0.842543i | \(-0.681058\pi\) | ||||
−0.538629 | + | 0.842543i | \(0.681058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.04251e75 | −1.47364 | ||||||||
\(176\) | −5.80589e74 | −0.346094 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.37366e74 | 0.137731 | ||||||||
\(179\) | 5.16237e75 | 1.74692 | 0.873459 | − | 0.486897i | \(-0.161871\pi\) | ||||
0.873459 | + | 0.486897i | \(0.161871\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.57317e75 | −1.76622 | −0.883112 | − | 0.469163i | \(-0.844556\pi\) | ||||
−0.883112 | + | 0.469163i | \(0.844556\pi\) | |||||||
\(182\) | −2.30580e75 | −0.447126 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.09777e75 | −0.147609 | ||||||||
\(185\) | 1.73995e75 | 0.195112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.52763e75 | 0.354142 | ||||||||
\(188\) | 1.01287e75 | 0.0662620 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.33307e76 | 0.611797 | ||||||||
\(191\) | 3.59630e75 | 0.138432 | 0.0692162 | − | 0.997602i | \(-0.477950\pi\) | ||||
0.0692162 | + | 0.997602i | \(0.477950\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.38661e75 | −0.173420 | −0.0867102 | − | 0.996234i | \(-0.527635\pi\) | ||||
−0.0867102 | + | 0.996234i | \(0.527635\pi\) | |||||||
\(194\) | −5.53060e76 | −1.26303 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.52590e75 | −0.105697 | ||||||||
\(197\) | 1.09438e77 | 1.49468 | 0.747340 | − | 0.664442i | \(-0.231331\pi\) | ||||
0.747340 | + | 0.664442i | \(0.231331\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.77255e77 | 1.72592 | 0.862960 | − | 0.505272i | \(-0.168608\pi\) | ||||
0.862960 | + | 0.505272i | \(0.168608\pi\) | |||||||
\(200\) | −1.11032e77 | −0.913996 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.56155e77 | 0.921054 | ||||||||
\(203\) | 6.38372e76 | 0.319122 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.52670e77 | 0.549542 | ||||||||
\(206\) | −1.27303e77 | −0.389301 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.17732e77 | −0.260479 | ||||||||
\(209\) | 3.72156e77 | 0.701172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.93889e77 | 0.265516 | 0.132758 | − | 0.991148i | \(-0.457617\pi\) | ||||
0.132758 | + | 0.991148i | \(0.457617\pi\) | |||||||
\(212\) | 4.98289e76 | 0.0582412 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.39332e78 | −1.18902 | ||||||||
\(215\) | −4.90404e77 | −0.357986 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.31069e78 | −1.77222 | ||||||||
\(218\) | 1.57285e78 | 0.721762 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.20461e76 | 0.00745028 | ||||||||
\(221\) | 9.18113e77 | 0.266535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.20956e78 | 0.474343 | 0.237172 | − | 0.971468i | \(-0.423780\pi\) | ||||
0.237172 | + | 0.971468i | \(0.423780\pi\) | |||||||
\(224\) | −1.08386e78 | −0.200293 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.62259e78 | 0.222626 | ||||||||
\(227\) | −1.52442e79 | −1.80401 | −0.902006 | − | 0.431724i | \(-0.857906\pi\) | ||||
−0.902006 | + | 0.431724i | \(0.857906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.58294e78 | −0.757090 | −0.378545 | − | 0.925583i | \(-0.623575\pi\) | ||||
−0.378545 | + | 0.925583i | \(0.623575\pi\) | |||||||
\(230\) | −6.07878e77 | −0.0463376 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.47023e78 | 0.197929 | ||||||||
\(233\) | −3.80136e79 | −1.87722 | −0.938611 | − | 0.344976i | \(-0.887887\pi\) | ||||
−0.938611 | + | 0.344976i | \(0.887887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.82959e78 | 0.364554 | ||||||||
\(236\) | 2.27137e78 | 0.0730694 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.34394e79 | −1.53827 | ||||||||
\(239\) | 3.96682e79 | 0.835820 | 0.417910 | − | 0.908489i | \(-0.362763\pi\) | ||||
0.417910 | + | 0.908489i | \(0.362763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.56846e79 | 0.887492 | 0.443746 | − | 0.896153i | \(-0.353649\pi\) | ||||
0.443746 | + | 0.896153i | \(0.353649\pi\) | |||||||
\(242\) | 6.03095e79 | 0.836703 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.15247e78 | 0.0437267 | ||||||||
\(245\) | −6.33321e79 | −0.581514 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.54658e79 | 0.527718 | ||||||||
\(248\) | −1.79971e80 | −1.09918 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.30630e80 | −0.609609 | ||||||||
\(251\) | 1.96582e80 | 0.802553 | 0.401277 | − | 0.915957i | \(-0.368567\pi\) | ||||
0.401277 | + | 0.915957i | \(0.368567\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.69703e79 | −0.0531069 | ||||||||
\(254\) | −1.42438e80 | −0.390567 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.57774e79 | −0.180856 | ||||||||
\(257\) | −1.75539e80 | −0.324799 | −0.162399 | − | 0.986725i | \(-0.551923\pi\) | ||||
−0.162399 | + | 0.986725i | \(0.551923\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.80608e80 | −0.971304 | ||||||||
\(260\) | 4.47052e78 | 0.00560726 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.22882e80 | 0.895473 | ||||||||
\(263\) | 3.81404e79 | 0.0325737 | 0.0162869 | − | 0.999867i | \(-0.494816\pi\) | ||||
0.0162869 | + | 0.999867i | \(0.494816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.83576e80 | 0.320426 | ||||||||
\(266\) | −5.21451e81 | −3.04564 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.36933e78 | −0.00289453 | ||||||||
\(269\) | −3.78256e81 | −1.51735 | −0.758673 | − | 0.651472i | \(-0.774152\pi\) | ||||
−0.758673 | + | 0.651472i | \(0.774152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.36695e81 | −1.67979 | −0.839897 | − | 0.542746i | \(-0.817385\pi\) | ||||
−0.839897 | + | 0.542746i | \(0.817385\pi\) | |||||||
\(272\) | −3.23916e81 | −0.896135 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.13197e81 | −0.894363 | ||||||||
\(275\) | −1.71643e81 | −0.328838 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.61409e81 | −0.242580 | −0.121290 | − | 0.992617i | \(-0.538703\pi\) | ||||
−0.121290 | + | 0.992617i | \(0.538703\pi\) | |||||||
\(278\) | 4.13686e81 | 0.551023 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.41375e81 | −0.567158 | ||||||||
\(281\) | −4.09174e80 | −0.0380405 | −0.0190203 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190203 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.49274e82 | −1.82739 | −0.913696 | − | 0.406399i | \(-0.866784\pi\) | ||||
−0.913696 | + | 0.406399i | \(0.866784\pi\) | |||||||
\(284\) | 1.26481e81 | 0.0823875 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.93769e81 | −0.0997749 | ||||||||
\(287\) | −5.97195e82 | −2.73572 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.28719e81 | −0.0830281 | ||||||||
\(290\) | 1.92160e81 | 0.0621342 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.56131e81 | 0.0657865 | ||||||||
\(293\) | −3.33237e82 | −0.763286 | −0.381643 | − | 0.924310i | \(-0.624642\pi\) | ||||
−0.381643 | + | 0.924310i | \(0.624642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.20430e82 | 0.402007 | ||||||||
\(296\) | −3.69982e82 | −0.602433 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00808e82 | 0.390881 | ||||||||
\(299\) | −3.44123e81 | −0.0399695 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.91829e83 | 1.78212 | ||||||||
\(302\) | −1.07184e83 | −0.891040 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.66248e83 | −1.77428 | ||||||||
\(305\) | 4.02986e82 | 0.240572 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.72597e83 | 0.827749 | 0.413875 | − | 0.910334i | \(-0.364175\pi\) | ||||
0.413875 | + | 0.910334i | \(0.364175\pi\) | |||||||
\(308\) | −8.62370e81 | −0.0370889 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.96569e82 | −0.345057 | ||||||||
\(311\) | −6.02046e83 | −1.87136 | −0.935678 | − | 0.352854i | \(-0.885211\pi\) | ||||
−0.935678 | + | 0.352854i | \(0.885211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.50740e83 | −1.88258 | −0.941291 | − | 0.337595i | \(-0.890386\pi\) | ||||
−0.941291 | + | 0.337595i | \(0.890386\pi\) | |||||||
\(314\) | −4.86668e82 | −0.109670 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.51000e82 | −0.0457253 | ||||||||
\(317\) | 5.32909e83 | 0.873309 | 0.436654 | − | 0.899629i | \(-0.356163\pi\) | ||||
0.436654 | + | 0.899629i | \(0.356163\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.36458e82 | 0.0712112 | ||||||||
\(320\) | −2.93275e83 | −0.350550 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.37781e83 | 0.230678 | ||||||||
\(323\) | 2.07629e84 | 1.81553 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.48059e83 | −0.247491 | ||||||||
\(326\) | 7.58605e83 | 0.486660 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.24638e84 | −1.69678 | ||||||||
\(329\) | −3.84500e84 | −1.81482 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.64253e83 | −0.217388 | −0.108694 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108694 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(332\) | 3.19129e83 | 0.111132 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.31624e84 | 1.51390 | ||||||||
\(335\) | −6.18126e82 | −0.0159249 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.29452e84 | 1.75061 | 0.875305 | − | 0.483571i | \(-0.160660\pi\) | ||||
0.875305 | + | 0.483571i | \(0.160660\pi\) | |||||||
\(338\) | 4.67880e84 | 0.894179 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.22997e83 | 0.0192909 | ||||||||
\(341\) | −2.78215e84 | −0.395465 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.05906e85 | 1.23756 | ||||||||
\(344\) | 1.04279e85 | 1.10533 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.19623e85 | 1.04416 | ||||||||
\(347\) | 2.06934e85 | 1.63981 | 0.819907 | − | 0.572497i | \(-0.194025\pi\) | ||||
0.819907 | + | 0.572497i | \(0.194025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.67071e85 | −1.09207 | −0.546035 | − | 0.837762i | \(-0.683863\pi\) | ||||
−0.546035 | + | 0.837762i | \(0.683863\pi\) | |||||||
\(350\) | 2.40500e85 | 1.42836 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.10829e83 | −0.0446949 | ||||||||
\(353\) | 1.33918e85 | 0.597565 | 0.298783 | − | 0.954321i | \(-0.403419\pi\) | ||||
0.298783 | + | 0.954321i | \(0.403419\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.22746e85 | 0.453272 | ||||||||
\(356\) | 2.55858e83 | 0.00859851 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.07855e85 | −1.69324 | ||||||||
\(359\) | −2.93947e85 | −0.745770 | −0.372885 | − | 0.927878i | \(-0.621631\pi\) | ||||
−0.372885 | + | 0.927878i | \(0.621631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23186e86 | 2.59460 | ||||||||
\(362\) | 8.91720e85 | 1.71195 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.74871e84 | −0.0279140 | ||||||||
\(365\) | 2.48568e85 | 0.361938 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.43979e85 | −0.417079 | −0.208540 | − | 0.978014i | \(-0.566871\pi\) | ||||
−0.208540 | + | 0.978014i | \(0.566871\pi\) | |||||||
\(368\) | 1.21409e85 | 0.134384 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.04874e85 | −0.189116 | ||||||||
\(371\) | −1.89158e86 | −1.59514 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.47551e85 | −0.596926 | −0.298463 | − | 0.954421i | \(-0.596474\pi\) | ||||
−0.298463 | + | 0.954421i | \(0.596474\pi\) | |||||||
\(374\) | −5.33115e85 | −0.343260 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.09016e86 | −1.12561 | ||||||||
\(377\) | 1.08783e85 | 0.0535952 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.80867e86 | 1.57167 | 0.785833 | − | 0.618439i | \(-0.212234\pi\) | ||||
0.785833 | + | 0.618439i | \(0.212234\pi\) | |||||||
\(380\) | 1.01100e85 | 0.0381944 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.23454e85 | −0.134179 | ||||||||
\(383\) | −3.86709e86 | −1.12260 | −0.561301 | − | 0.827612i | \(-0.689699\pi\) | ||||
−0.561301 | + | 0.827612i | \(0.689699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.36906e85 | −0.204053 | ||||||||
\(386\) | 7.52005e85 | 0.168092 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.19439e85 | −0.0788509 | ||||||||
\(389\) | −3.99336e86 | −0.688694 | −0.344347 | − | 0.938842i | \(-0.611900\pi\) | ||||
−0.344347 | + | 0.938842i | \(0.611900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.46786e85 | −0.137509 | ||||||||
\(392\) | 1.34669e87 | 1.79550 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.28860e87 | −1.44875 | ||||||||
\(395\) | −2.43588e86 | −0.251567 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.04225e85 | −0.0265285 | −0.0132642 | − | 0.999912i | \(-0.504222\pi\) | ||||
−0.0132642 | + | 0.999912i | \(0.504222\pi\) | |||||||
\(398\) | −2.08713e87 | −1.67289 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.22797e87 | 0.832106 | ||||||||
\(401\) | 9.25408e84 | 0.00576762 | 0.00288381 | − | 0.999996i | \(-0.499082\pi\) | ||||
0.00288381 | + | 0.999996i | \(0.499082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.64164e86 | −0.297636 | ||||||||
\(404\) | 1.18428e86 | 0.0575013 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.51666e86 | −0.309316 | ||||||||
\(407\) | −5.71951e86 | −0.216744 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.19777e87 | 0.706725 | 0.353363 | − | 0.935486i | \(-0.385038\pi\) | ||||
0.353363 | + | 0.935486i | \(0.385038\pi\) | |||||||
\(410\) | −1.79765e87 | −0.532655 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.65461e85 | −0.0243040 | ||||||||
\(413\) | −8.62247e87 | −2.00127 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.09706e87 | 0.611419 | ||||||||
\(416\) | −1.84698e86 | −0.0336384 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.38203e87 | −0.679626 | ||||||||
\(419\) | 7.19150e86 | 0.102956 | 0.0514778 | − | 0.998674i | \(-0.483607\pi\) | ||||
0.0514778 | + | 0.998674i | \(0.483607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.30697e87 | −0.281574 | −0.140787 | − | 0.990040i | \(-0.544963\pi\) | ||||
−0.140787 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(422\) | −2.28299e87 | −0.257357 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.02828e88 | −0.989357 | ||||||||
\(425\) | −9.57613e87 | −0.851454 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.57634e88 | −1.19761 | ||||||||
\(428\) | −1.05669e87 | −0.0742302 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.77437e87 | 0.346985 | ||||||||
\(431\) | 3.10236e88 | 1.72466 | 0.862329 | − | 0.506349i | \(-0.169005\pi\) | ||||
0.862329 | + | 0.506349i | \(0.169005\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.16319e88 | −0.553739 | −0.276870 | − | 0.960908i | \(-0.589297\pi\) | ||||
−0.276870 | + | 0.960908i | \(0.589297\pi\) | |||||||
\(434\) | 3.89824e88 | 1.71776 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.19284e87 | 0.0450595 | ||||||||
\(437\) | −7.78227e87 | −0.272256 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.19420e88 | 1.85962 | 0.929810 | − | 0.368041i | \(-0.119971\pi\) | ||||
0.929810 | + | 0.368041i | \(0.119971\pi\) | |||||||
\(440\) | −4.54947e87 | −0.126560 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.08105e88 | −0.258345 | ||||||||
\(443\) | 2.39920e88 | 0.531548 | 0.265774 | − | 0.964035i | \(-0.414373\pi\) | ||||
0.265774 | + | 0.964035i | \(0.414373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48303e87 | 0.0473065 | ||||||||
\(446\) | −2.60169e88 | −0.459768 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.14719e89 | 1.74511 | ||||||||
\(449\) | 9.08623e88 | 1.28272 | 0.641359 | − | 0.767241i | \(-0.278371\pi\) | ||||
0.641359 | + | 0.767241i | \(0.278371\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.01855e88 | −0.610469 | ||||||||
\(452\) | 1.23057e87 | 0.0138985 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.79497e89 | 1.74858 | ||||||||
\(455\) | −1.69708e88 | −0.153575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.32640e88 | −0.103629 | −0.0518144 | − | 0.998657i | \(-0.516500\pi\) | ||||
−0.0518144 | + | 0.998657i | \(0.516500\pi\) | |||||||
\(458\) | 1.01062e89 | 0.733826 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.61013e86 | −0.00289285 | ||||||||
\(461\) | 2.12429e89 | 1.23946 | 0.619729 | − | 0.784816i | \(-0.287242\pi\) | ||||
0.619729 | + | 0.784816i | \(0.287242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44696e89 | −0.730288 | −0.365144 | − | 0.930951i | \(-0.618980\pi\) | ||||
−0.365144 | + | 0.930951i | \(0.618980\pi\) | |||||||
\(464\) | −3.83793e88 | −0.180196 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.47600e89 | 1.81954 | ||||||||
\(467\) | −5.46311e88 | −0.206692 | −0.103346 | − | 0.994645i | \(-0.532955\pi\) | ||||
−0.103346 | + | 0.994645i | \(0.532955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.41790e88 | 0.0792771 | ||||||||
\(470\) | −1.15741e89 | −0.353352 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.68722e89 | −1.24125 | ||||||||
\(473\) | 1.61204e89 | 0.397675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.87126e89 | −1.68581 | ||||||||
\(476\) | −4.81123e88 | −0.0960337 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.67082e89 | −0.810137 | ||||||||
\(479\) | 4.23497e89 | 0.684873 | 0.342437 | − | 0.939541i | \(-0.388748\pi\) | ||||
0.342437 | + | 0.939541i | \(0.388748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.15980e89 | −0.163126 | ||||||||
\(482\) | −6.55671e89 | −0.860221 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.57386e88 | 0.0522352 | ||||||||
\(485\) | −4.07054e89 | −0.433815 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.84541e89 | −0.449894 | −0.224947 | − | 0.974371i | \(-0.572221\pi\) | ||||
−0.224947 | + | 0.974371i | \(0.572221\pi\) | |||||||
\(488\) | −8.56908e89 | −0.742797 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.45718e89 | 0.563645 | ||||||||
\(491\) | 2.13083e89 | 0.150424 | 0.0752121 | − | 0.997168i | \(-0.476037\pi\) | ||||
0.0752121 | + | 0.997168i | \(0.476037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.99295e89 | 0.184386 | ||||||||
\(494\) | −8.88589e89 | −0.511503 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.99040e90 | 1.00070 | ||||||||
\(497\) | −4.80142e90 | −2.25648 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.80425e90 | 0.741186 | 0.370593 | − | 0.928795i | \(-0.379154\pi\) | ||||
0.370593 | + | 0.928795i | \(0.379154\pi\) | |||||||
\(500\) | −9.90693e88 | −0.0380578 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.31470e90 | −0.777893 | ||||||||
\(503\) | 1.06464e90 | 0.334714 | 0.167357 | − | 0.985896i | \(-0.446477\pi\) | ||||
0.167357 | + | 0.985896i | \(0.446477\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.14931e90 | 0.316355 | ||||||||
\(506\) | 1.99820e89 | 0.0514751 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.08025e89 | −0.0243831 | ||||||||
\(509\) | −3.06397e90 | −0.647498 | −0.323749 | − | 0.946143i | \(-0.604943\pi\) | ||||
−0.323749 | + | 0.946143i | \(0.604943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.72314e90 | −1.80180 | ||||||||
\(512\) | 6.19406e90 | 1.07506 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.06692e90 | 0.314818 | ||||||||
\(515\) | −9.36953e89 | −0.133714 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.23116e90 | −0.404972 | ||||||||
\(518\) | 8.01397e90 | 0.941458 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.22541e89 | −0.0952519 | ||||||||
\(521\) | −2.01669e90 | −0.195243 | −0.0976213 | − | 0.995224i | \(-0.531123\pi\) | ||||
−0.0976213 | + | 0.995224i | \(0.531123\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.17519e91 | 1.00069 | 0.500346 | − | 0.865825i | \(-0.333206\pi\) | ||||
0.500346 | + | 0.865825i | \(0.333206\pi\) | |||||||
\(524\) | 6.99911e89 | 0.0559043 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.49092e89 | −0.0315728 | ||||||||
\(527\) | −1.55218e91 | −1.02397 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.68545e91 | −0.979379 | ||||||||
\(530\) | −5.69397e90 | −0.310580 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.95467e90 | −0.190139 | ||||||||
\(533\) | −1.01766e91 | −0.459453 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.02549e91 | −0.408393 | ||||||||
\(536\) | 1.31438e90 | 0.0491701 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.45386e91 | 1.47072 | ||||||||
\(539\) | 2.08184e91 | 0.645986 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.06689e91 | 0.566512 | 0.283256 | − | 0.959044i | \(-0.408585\pi\) | ||||
0.283256 | + | 0.959044i | \(0.408585\pi\) | |||||||
\(542\) | 6.31943e91 | 1.62818 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.08159e90 | −0.115728 | ||||||||
\(545\) | 1.15762e91 | 0.247904 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.29187e91 | −0.623545 | −0.311773 | − | 0.950157i | \(-0.600923\pi\) | ||||
−0.311773 | + | 0.950157i | \(0.600923\pi\) | |||||||
\(548\) | −3.13368e90 | −0.0558349 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.02105e91 | 0.318733 | ||||||||
\(551\) | 2.46010e91 | 0.365069 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.52835e91 | 1.25235 | ||||||||
\(554\) | 1.90054e91 | 0.235126 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.13738e90 | 0.0344003 | ||||||||
\(557\) | −9.99717e90 | −0.103211 | −0.0516057 | − | 0.998668i | \(-0.516434\pi\) | ||||
−0.0516057 | + | 0.998668i | \(0.516434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.26890e91 | 0.299300 | ||||||||
\(560\) | 5.98739e91 | 0.516344 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.81791e90 | 0.0368716 | ||||||||
\(563\) | 9.45819e91 | 0.681988 | 0.340994 | − | 0.940065i | \(-0.389236\pi\) | ||||
0.340994 | + | 0.940065i | \(0.389236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.19423e91 | 0.0764654 | ||||||||
\(566\) | 2.93513e92 | 1.77124 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.61008e92 | −1.39954 | ||||||||
\(569\) | −6.37286e91 | −0.322161 | −0.161081 | − | 0.986941i | \(-0.551498\pi\) | ||||
−0.161081 | + | 0.986941i | \(0.551498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.06623e89 | 0.00362544 | 0.00181272 | − | 0.999998i | \(-0.499423\pi\) | ||||
0.00181272 | + | 0.999998i | \(0.499423\pi\) | |||||||
\(572\) | −1.46954e90 | −0.00622893 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.03180e92 | 2.65166 | ||||||||
\(575\) | 3.58929e91 | 0.127684 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.61473e92 | −1.46136 | −0.730679 | − | 0.682721i | \(-0.760796\pi\) | ||||
−0.730679 | + | 0.682721i | \(0.760796\pi\) | |||||||
\(578\) | 2.69311e91 | 0.0804768 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.45734e90 | 0.00387903 | ||||||||
\(581\) | −1.21147e93 | −3.04376 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.58960e92 | −0.355952 | ||||||||
\(584\) | −5.28555e92 | −1.11753 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.92377e92 | 0.739832 | ||||||||
\(587\) | −5.69889e92 | −1.01488 | −0.507439 | − | 0.861687i | \(-0.669408\pi\) | ||||
−0.507439 | + | 0.861687i | \(0.669408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.27584e93 | −2.02738 | ||||||||
\(590\) | −2.59550e92 | −0.389654 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.09185e92 | 0.548458 | ||||||||
\(593\) | 3.99789e92 | 0.506406 | 0.253203 | − | 0.967413i | \(-0.418516\pi\) | ||||
0.253203 | + | 0.967413i | \(0.418516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.66917e92 | −0.528350 | ||||||||
\(596\) | 2.28132e91 | 0.0244027 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.05195e91 | 0.0387414 | ||||||||
\(599\) | 2.15668e93 | 1.94979 | 0.974893 | − | 0.222672i | \(-0.0714779\pi\) | ||||
0.974893 | + | 0.222672i | \(0.0714779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.79477e93 | −1.45115 | −0.725577 | − | 0.688141i | \(-0.758427\pi\) | ||||
−0.725577 | + | 0.688141i | \(0.758427\pi\) | |||||||
\(602\) | −2.25874e93 | −1.72736 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.12881e91 | −0.0556275 | ||||||||
\(605\) | 4.43881e92 | 0.287383 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.96333e92 | 0.403641 | 0.201821 | − | 0.979422i | \(-0.435314\pi\) | ||||
0.201821 | + | 0.979422i | \(0.435314\pi\) | |||||||
\(608\) | −4.17690e92 | −0.229131 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.74504e92 | −0.233180 | ||||||||
\(611\) | −6.55215e92 | −0.304792 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.53478e93 | −1.05685 | −0.528427 | − | 0.848979i | \(-0.677218\pi\) | ||||
−0.528427 | + | 0.848979i | \(0.677218\pi\) | |||||||
\(614\) | −2.03229e93 | −0.802314 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.77960e93 | 0.630039 | ||||||||
\(617\) | 1.32260e93 | 0.443480 | 0.221740 | − | 0.975106i | \(-0.428826\pi\) | ||||
0.221740 | + | 0.975106i | \(0.428826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.63639e93 | 0.492324 | 0.246162 | − | 0.969229i | \(-0.420830\pi\) | ||||
0.246162 | + | 0.969229i | \(0.420830\pi\) | |||||||
\(620\) | −7.55796e91 | −0.0215419 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.08892e93 | 1.81385 | ||||||||
\(623\) | −9.71275e92 | −0.235501 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.12141e93 | 0.679783 | ||||||||
\(626\) | 8.83975e93 | 1.82473 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.69088e91 | −0.00684671 | ||||||||
\(629\) | −3.19097e93 | −0.561210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.46704e93 | 0.548247 | 0.274123 | − | 0.961695i | \(-0.411612\pi\) | ||||
0.274123 | + | 0.961695i | \(0.411612\pi\) | |||||||
\(632\) | 5.17966e93 | 0.776747 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.27486e93 | −0.846474 | ||||||||
\(635\) | −1.04835e93 | −0.134149 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.22155e93 | 0.486184 | ||||||||
\(638\) | −6.31665e92 | −0.0690230 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.04432e93 | 0.299545 | ||||||||
\(641\) | −5.70835e93 | −0.533048 | −0.266524 | − | 0.963828i | \(-0.585875\pi\) | ||||
−0.266524 | + | 0.963828i | \(0.585875\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.13110e93 | −0.0951551 | −0.0475776 | − | 0.998868i | \(-0.515150\pi\) | ||||
−0.0475776 | + | 0.998868i | \(0.515150\pi\) | |||||||
\(644\) | 1.80333e92 | 0.0144012 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.44477e94 | −1.75974 | ||||||||
\(647\) | 2.31289e94 | 1.58074 | 0.790371 | − | 0.612629i | \(-0.209888\pi\) | ||||
0.790371 | + | 0.612629i | \(0.209888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.24592e93 | −0.446577 | ||||||||
\(650\) | 4.09829e93 | 0.239886 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.75324e92 | 0.0303821 | ||||||||
\(653\) | −1.79330e94 | −0.899627 | −0.449813 | − | 0.893123i | \(-0.648509\pi\) | ||||
−0.449813 | + | 0.893123i | \(0.648509\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.79245e93 | 0.307569 | ||||||||
\(656\) | 3.59037e94 | 1.54476 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.52738e94 | 1.75906 | ||||||||
\(659\) | 3.65704e94 | 1.35042 | 0.675210 | − | 0.737626i | \(-0.264053\pi\) | ||||
0.675210 | + | 0.737626i | \(0.264053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.70005e93 | −0.0567170 | −0.0283585 | − | 0.999598i | \(-0.509028\pi\) | ||||
−0.0283585 | + | 0.999598i | \(0.509028\pi\) | |||||||
\(662\) | 6.64392e93 | 0.210708 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.58559e94 | −1.88784 | ||||||||
\(665\) | −3.83790e94 | −1.04609 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.12180e93 | −0.0276504 | ||||||||
\(668\) | 4.03183e93 | 0.0945128 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.27826e92 | 0.0154355 | ||||||||
\(671\) | −1.32468e94 | −0.267244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.91904e94 | 0.898205 | 0.449103 | − | 0.893480i | \(-0.351744\pi\) | ||||
0.449103 | + | 0.893480i | \(0.351744\pi\) | |||||||
\(674\) | −9.76656e94 | −1.69682 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.54839e93 | 0.0558235 | ||||||||
\(677\) | 9.40701e93 | 0.140842 | 0.0704208 | − | 0.997517i | \(-0.477566\pi\) | ||||
0.0704208 | + | 0.997517i | \(0.477566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.59226e95 | 2.15961 | ||||||||
\(680\) | −2.53819e94 | −0.327699 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.27590e94 | 0.383313 | ||||||||
\(683\) | 6.94762e94 | 0.774003 | 0.387001 | − | 0.922079i | \(-0.373511\pi\) | ||||
0.387001 | + | 0.922079i | \(0.373511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.04115e94 | −0.307188 | ||||||||
\(686\) | −1.24701e95 | −1.19954 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.15329e95 | −1.00629 | ||||||||
\(689\) | −3.22339e94 | −0.267898 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.28074e95 | 0.965929 | 0.482965 | − | 0.875640i | \(-0.339560\pi\) | ||||
0.482965 | + | 0.875640i | \(0.339560\pi\) | |||||||
\(692\) | 9.07218e93 | 0.0651865 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.43659e95 | −1.58943 | ||||||||
\(695\) | 3.04474e94 | 0.189260 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.79989e95 | −1.58068 | ||||||||
\(698\) | 1.96722e95 | 1.05851 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.82395e94 | 0.0891720 | ||||||||
\(701\) | −2.80240e95 | −1.30610 | −0.653049 | − | 0.757316i | \(-0.726510\pi\) | ||||
−0.653049 | + | 0.757316i | \(0.726510\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.62287e95 | −1.11115 | ||||||||
\(704\) | 9.64046e94 | 0.389416 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.57684e95 | −0.579203 | ||||||||
\(707\) | −4.49570e95 | −1.57488 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.25694e95 | 0.719235 | 0.359618 | − | 0.933100i | \(-0.382907\pi\) | ||||
0.359618 | + | 0.933100i | \(0.382907\pi\) | |||||||
\(710\) | −1.44531e95 | −0.439344 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.27991e94 | −0.146065 | ||||||||
\(713\) | 5.81783e94 | 0.153554 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.42615e94 | −0.0342698 | ||||||||
\(716\) | −4.60996e94 | −0.105709 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.46114e95 | 0.722854 | ||||||||
\(719\) | 9.75088e95 | 1.94368 | 0.971842 | − | 0.235632i | \(-0.0757160\pi\) | ||||
0.971842 | + | 0.235632i | \(0.0757160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.66504e95 | 0.665652 | ||||||||
\(722\) | −1.45048e96 | −2.51488 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.76278e94 | 0.106877 | ||||||||
\(725\) | −1.13463e95 | −0.171211 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.69861e95 | −0.784090 | −0.392045 | − | 0.919946i | \(-0.628232\pi\) | ||||
−0.392045 | + | 0.919946i | \(0.628232\pi\) | |||||||
\(728\) | 3.60866e95 | 0.474182 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.92682e95 | −0.350817 | ||||||||
\(731\) | 8.99373e95 | 1.02969 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.44503e95 | 0.568876 | 0.284438 | − | 0.958694i | \(-0.408193\pi\) | ||||
0.284438 | + | 0.958694i | \(0.408193\pi\) | |||||||
\(734\) | 4.05025e95 | 0.404263 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.90466e94 | 0.0173545 | ||||||||
\(737\) | 2.03189e94 | 0.0176905 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.49500e96 | 1.18864 | 0.594321 | − | 0.804228i | \(-0.297421\pi\) | ||||
0.594321 | + | 0.804228i | \(0.297421\pi\) | |||||||
\(740\) | −1.55376e94 | −0.0118065 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.22729e96 | 1.54613 | ||||||||
\(743\) | 1.54879e96 | 1.02770 | 0.513852 | − | 0.857879i | \(-0.328218\pi\) | ||||
0.513852 | + | 0.857879i | \(0.328218\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.21396e95 | 0.134256 | ||||||||
\(746\) | 9.97968e95 | 0.578583 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.04314e94 | −0.0214296 | ||||||||
\(749\) | 4.01136e96 | 2.03306 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.73924e95 | −0.405075 | −0.202538 | − | 0.979274i | \(-0.564919\pi\) | ||||
−0.202538 | + | 0.979274i | \(0.564919\pi\) | |||||||
\(752\) | 2.31164e96 | 1.02476 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.28089e95 | −0.0519483 | ||||||||
\(755\) | −7.88878e95 | −0.306046 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.73020e95 | −0.167945 | −0.0839726 | − | 0.996468i | \(-0.526761\pi\) | ||||
−0.0839726 | + | 0.996468i | \(0.526761\pi\) | |||||||
\(758\) | −4.48461e96 | −1.52337 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.08630e96 | −0.648817 | ||||||||
\(761\) | 8.82131e95 | 0.262511 | 0.131255 | − | 0.991349i | \(-0.458099\pi\) | ||||
0.131255 | + | 0.991349i | \(0.458099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.52822e96 | −1.23411 | ||||||||
\(764\) | −3.21147e94 | −0.00837675 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.55339e96 | 1.08811 | ||||||||
\(767\) | −1.46933e96 | −0.336104 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00203e96 | −0.419699 | −0.209849 | − | 0.977734i | \(-0.567297\pi\) | ||||
−0.209849 | + | 0.977734i | \(0.567297\pi\) | |||||||
\(770\) | 9.85433e95 | 0.197783 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.70319e94 | 0.0104939 | ||||||||
\(773\) | −4.95099e96 | −0.872326 | −0.436163 | − | 0.899868i | \(-0.643663\pi\) | ||||
−0.436163 | + | 0.899868i | \(0.643663\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.88436e96 | 0.950807 | ||||||||
\(776\) | 8.65560e96 | 1.33946 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.70206e96 | 0.667532 | ||||||||
\(779\) | −2.30142e97 | −3.12961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.03489e96 | −0.503526 | ||||||||
\(782\) | 1.11481e96 | 0.133283 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.48939e97 | −1.63463 | ||||||||
\(785\) | −3.58190e95 | −0.0376686 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.38948e96 | 0.230754 | 0.115377 | − | 0.993322i | \(-0.463192\pi\) | ||||
0.115377 | + | 0.993322i | \(0.463192\pi\) | |||||||
\(788\) | −9.77269e95 | −0.0904453 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.86819e96 | 0.243837 | ||||||||
\(791\) | −4.67142e96 | −0.380660 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.68620e96 | −0.201134 | ||||||||
\(794\) | 3.58216e95 | 0.0257133 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.58287e96 | −0.104438 | ||||||||
\(797\) | −1.68047e96 | −0.106311 | −0.0531555 | − | 0.998586i | \(-0.516928\pi\) | ||||
−0.0531555 | + | 0.998586i | \(0.516928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.80269e97 | −1.04859 | ||||||||
\(800\) | 1.92644e96 | 0.107459 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.08964e95 | −0.00559039 | ||||||||
\(803\) | −8.17087e96 | −0.402066 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.75008e96 | 0.0792311 | ||||||||
\(806\) | 6.64287e96 | 0.288491 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.44389e97 | −0.976788 | ||||||||
\(809\) | 2.72314e97 | 1.04422 | 0.522112 | − | 0.852877i | \(-0.325144\pi\) | ||||
0.522112 | + | 0.852877i | \(0.325144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.37416e97 | 0.838129 | 0.419064 | − | 0.907957i | \(-0.362358\pi\) | ||||
0.419064 | + | 0.907957i | \(0.362358\pi\) | |||||||
\(812\) | −5.70062e95 | −0.0193106 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.73457e96 | 0.210084 | ||||||||
\(815\) | 5.58336e96 | 0.167154 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.39255e97 | 2.03871 | ||||||||
\(818\) | −2.58781e97 | −0.685009 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.36334e96 | −0.0332536 | ||||||||
\(821\) | −3.28742e97 | −0.769768 | −0.384884 | − | 0.922965i | \(-0.625759\pi\) | ||||
−0.384884 | + | 0.922965i | \(0.625759\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.10619e97 | −1.31788 | −0.658940 | − | 0.752196i | \(-0.728995\pi\) | ||||
−0.658940 | + | 0.752196i | \(0.728995\pi\) | |||||||
\(824\) | 1.99234e97 | 0.412858 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.01527e98 | 1.93977 | ||||||||
\(827\) | −8.44596e97 | −1.54958 | −0.774791 | − | 0.632217i | \(-0.782145\pi\) | ||||
−0.774791 | + | 0.632217i | \(0.782145\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.39242e97 | −1.58928 | −0.794641 | − | 0.607080i | \(-0.792341\pi\) | ||||
−0.794641 | + | 0.607080i | \(0.792341\pi\) | |||||||
\(830\) | −3.64670e97 | −0.592631 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.95489e97 | 0.293083 | ||||||||
\(833\) | 1.16147e98 | 1.67264 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.91278e97 | 0.519982 | ||||||||
\(836\) | −3.32332e96 | −0.0424290 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.46780e96 | −0.0997920 | ||||||||
\(839\) | 7.34342e97 | 0.831520 | 0.415760 | − | 0.909474i | \(-0.363516\pi\) | ||||
0.415760 | + | 0.909474i | \(0.363516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.20996e97 | −0.962924 | ||||||||
\(842\) | 2.71639e97 | 0.272921 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.73141e96 | −0.0160668 | ||||||||
\(845\) | 3.44361e97 | 0.307125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.73631e98 | −1.43065 | ||||||||
\(848\) | 1.13723e98 | 0.900715 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.12756e98 | 0.825290 | ||||||||
\(851\) | 1.19602e97 | 0.0841589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.13590e97 | −0.0738833 | −0.0369417 | − | 0.999317i | \(-0.511762\pi\) | ||||
−0.0369417 | + | 0.999317i | \(0.511762\pi\) | |||||||
\(854\) | 1.85610e98 | 1.16081 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.18059e98 | 1.26097 | ||||||||
\(857\) | −1.84882e98 | −1.02810 | −0.514052 | − | 0.857759i | \(-0.671856\pi\) | ||||
−0.514052 | + | 0.857759i | \(0.671856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.66736e98 | 1.37186 | 0.685932 | − | 0.727666i | \(-0.259395\pi\) | ||||
0.685932 | + | 0.727666i | \(0.259395\pi\) | |||||||
\(860\) | 4.37927e96 | 0.0216622 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.65294e98 | −1.67166 | ||||||||
\(863\) | 1.57014e98 | 0.691158 | 0.345579 | − | 0.938390i | \(-0.387683\pi\) | ||||
0.345579 | + | 0.938390i | \(0.387683\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.80431e97 | 0.358637 | ||||||||
\(866\) | 1.36962e98 | 0.536724 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.95642e97 | 0.107240 | ||||||||
\(869\) | 8.00718e97 | 0.279458 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.12026e96 | 0.0133143 | ||||||||
\(872\) | −2.46157e98 | −0.765436 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.16340e97 | 0.263890 | ||||||||
\(875\) | 3.76083e98 | 1.04235 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.11089e97 | 0.0798726 | 0.0399363 | − | 0.999202i | \(-0.487284\pi\) | ||||
0.0399363 | + | 0.999202i | \(0.487284\pi\) | |||||||
\(878\) | −7.29350e98 | −1.80248 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.03153e97 | 0.115221 | ||||||||
\(881\) | 1.64669e98 | 0.363010 | 0.181505 | − | 0.983390i | \(-0.441903\pi\) | ||||
0.181505 | + | 0.983390i | \(0.441903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.37516e98 | 1.50691 | 0.753455 | − | 0.657499i | \(-0.228386\pi\) | ||||
0.753455 | + | 0.657499i | \(0.228386\pi\) | |||||||
\(884\) | −8.19867e96 | −0.0161285 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.82500e98 | −0.515215 | ||||||||
\(887\) | 1.04918e98 | 0.184250 | 0.0921251 | − | 0.995747i | \(-0.470634\pi\) | ||||
0.0921251 | + | 0.995747i | \(0.470634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.10078e98 | 0.667817 | ||||||||
\(890\) | −2.92369e97 | −0.0458529 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.97312e97 | −0.0287032 | ||||||||
\(893\) | −1.48175e99 | −2.07612 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.47384e98 | −0.581579 | ||||||||
\(896\) | −1.19083e99 | −1.49119 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.06988e99 | −1.24330 | ||||||||
\(899\) | −1.83911e98 | −0.205901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.86851e98 | −0.921659 | ||||||||
\(902\) | 5.90920e98 | 0.591711 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.53941e98 | −0.236097 | ||||||||
\(905\) | 6.56310e98 | 0.588005 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.65700e99 | −1.37873 | −0.689365 | − | 0.724414i | \(-0.742110\pi\) | ||||
−0.689365 | + | 0.724414i | \(0.742110\pi\) | |||||||
\(908\) | 1.36130e98 | 0.109163 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.99826e98 | 0.148856 | ||||||||
\(911\) | 1.04193e99 | 0.748120 | 0.374060 | − | 0.927405i | \(-0.377965\pi\) | ||||
0.374060 | + | 0.927405i | \(0.377965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.01806e99 | −0.679207 | ||||||||
\(914\) | 1.56179e98 | 0.100445 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.66450e97 | 0.0458127 | ||||||||
\(917\) | −2.65697e99 | −1.53114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.25435e98 | 0.174339 | 0.0871694 | − | 0.996194i | \(-0.472218\pi\) | ||||
0.0871694 | + | 0.996194i | \(0.472218\pi\) | |||||||
\(920\) | 9.51353e97 | 0.0491416 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.50129e99 | −1.20137 | ||||||||
\(923\) | −8.18196e98 | −0.378966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.20970e99 | 0.521111 | ||||||||
\(926\) | 1.70376e99 | 0.707848 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.02095e97 | −0.0232706 | ||||||||
\(929\) | −1.48846e99 | −0.554896 | −0.277448 | − | 0.960741i | \(-0.589489\pi\) | ||||
−0.277448 | + | 0.960741i | \(0.589489\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.54694e99 | 3.31169 | ||||||||
\(932\) | 3.39459e98 | 0.113594 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.43265e98 | 0.200341 | ||||||||
\(935\) | −3.92375e98 | −0.117900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.03087e98 | 0.196667 | 0.0983337 | − | 0.995153i | \(-0.468649\pi\) | ||||
0.0983337 | + | 0.995153i | \(0.468649\pi\) | |||||||
\(938\) | −2.84701e98 | −0.0768411 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.77775e97 | −0.0220597 | ||||||||
\(941\) | −2.70457e99 | −0.655913 | −0.327957 | − | 0.944693i | \(-0.606360\pi\) | ||||
−0.327957 | + | 0.944693i | \(0.606360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.04944e99 | 0.237038 | ||||||||
\(944\) | 5.18388e99 | 1.13004 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.89814e99 | −0.385456 | ||||||||
\(947\) | 2.68543e99 | 0.526367 | 0.263184 | − | 0.964746i | \(-0.415227\pi\) | ||||
0.263184 | + | 0.964746i | \(0.415227\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.65689e99 | −0.302605 | ||||||||
\(950\) | 9.26819e99 | 1.63401 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.92852e99 | 1.63135 | ||||||||
\(953\) | 3.67501e99 | 0.582970 | 0.291485 | − | 0.956575i | \(-0.405851\pi\) | ||||
0.291485 | + | 0.956575i | \(0.405851\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.11664e98 | −0.0460865 | ||||||||
\(956\) | −3.54234e98 | −0.0505767 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.98656e99 | −0.663829 | ||||||||
\(959\) | 1.18959e100 | 1.52924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.19659e99 | 0.143454 | ||||||||
\(962\) | 1.36564e99 | 0.158114 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.97259e98 | −0.0537035 | ||||||||
\(965\) | 5.53479e98 | 0.0577346 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.23398e100 | −1.20094 | −0.600471 | − | 0.799647i | \(-0.705020\pi\) | ||||
−0.600471 | + | 0.799647i | \(0.705020\pi\) | |||||||
\(968\) | −9.43867e99 | −0.887333 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.79295e99 | 0.420484 | ||||||||
\(971\) | −1.44651e100 | −1.22596 | −0.612982 | − | 0.790097i | \(-0.710030\pi\) | ||||
−0.612982 | + | 0.790097i | \(0.710030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.19100e100 | −0.942175 | ||||||||
\(974\) | 5.70534e99 | 0.436070 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.47706e99 | 0.676246 | ||||||||
\(977\) | 5.88645e99 | 0.405869 | 0.202934 | − | 0.979192i | \(-0.434952\pi\) | ||||
0.202934 | + | 0.979192i | \(0.434952\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.16215e98 | −0.0525514 | ||||||||
\(980\) | 5.65551e98 | 0.0351883 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.50899e99 | −0.145802 | ||||||||
\(983\) | −7.65934e99 | −0.430179 | −0.215089 | − | 0.976594i | \(-0.569004\pi\) | ||||
−0.215089 | + | 0.976594i | \(0.569004\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.48413e99 | −0.497604 | ||||||||
\(986\) | −3.52411e99 | −0.178720 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.73904e98 | −0.0319330 | ||||||||
\(989\) | −3.37099e99 | −0.154412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.25075e100 | −0.535432 | −0.267716 | − | 0.963498i | \(-0.586269\pi\) | ||||
−0.267716 | + | 0.963498i | \(0.586269\pi\) | |||||||
\(992\) | 3.12255e99 | 0.129231 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.65354e100 | 2.18714 | ||||||||
\(995\) | −1.53614e100 | −0.574588 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.47075e100 | −0.864055 | −0.432027 | − | 0.901861i | \(-0.642202\pi\) | ||||
−0.432027 | + | 0.901861i | \(0.642202\pi\) | |||||||
\(998\) | −2.12445e100 | −0.718411 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9.68.a.c.1.3 | 6 | ||
3.2 | odd | 2 | 3.68.a.b.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.68.a.b.1.4 | ✓ | 6 | 3.2 | odd | 2 | ||
9.68.a.c.1.3 | 6 | 1.1 | even | 1 | trivial |